//[TestMethod]
public void LoadInternalForce_trapezoidload_eulerbernoullybeam_dirY()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 =
//new Loads.(LoadCase.DefaultLoadCase, -Vector.K, w, CoordinationSystem.Global);
new Loads.PartialNonUniformLoad();
u1.CoordinationSystem = CoordinationSystem.Global;
u1.Direction = -Vector.K;
// u1.StartLocation = new double[] { };
// u1.EndLocation = new double[] { };
//u1.StartMagnitude
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = w * (length / 2 - x);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: mi, mz: 0);
var d = testFrc.FirstOrDefault(i => i.Item1 == DoF.Ry).Item2 + exactFrc.My;
Assert.IsTrue(d < 1e-5, "invalid value");
}
}
public void LoadInternalForce_uniformload_eulerbernoullybeam_endrelease()
{
//load internal force of beam with hinged ends should match the end releases
//if hinged then moment should be zero and so on
//added for issue#48
var w = 2.0;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.UniformLoad(LoadCase.DefaultLoadCase, -Vector.K, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(BeamDirection.Y, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
elm.NodalReleaseConditions[0] = Constraints.MovementFixed;
elm.NodalReleaseConditions[1] = Constraints.MovementFixed & Constraints.FixedRX;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var vi = -w * (length / 2 - x);
var mi = -w / 2 * (length * x - x * x);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: mi, mz: 0);
var d = testFrc - exactFrc;
var dm = d.My;
var df = d.Fz;
Assert.IsTrue(dm.FEquals(0, 1e-5), "invalid value");
Assert.IsTrue(df.FEquals(0, 1e-5), "invalid value");
}
}
public static void Run()
{
var model = new Model();
var l = 5.0;
var n1 = new Node()
{
Constraints = Constraints.Fixed
};
var n2 = new Node(l, 0, 0)
{
Constraints = Constraints.Fixed
};
var elm = new BarElement();
elm.Material = Materials.UniformIsotropicMaterial.CreateFromYoungPoisson(210e9, 0.25);
elm.Section = new Sections.UniformGeometric1DSection(SectionGenerator.GetRectangularSection(0.05, 0.05));
elm.Nodes[0] = n1;
elm.Nodes[1] = n2;
// elm.EndReleaseCondition = Constraints.RotationFixed;
var load = new Loads.UniformLoad(LoadCase.DefaultLoadCase, Vector.K, 100, CoordinationSystem.Global);
//var load2 = new Loads.ConcentratedLoad();// LoadCase.DefaultLoadCase, Vector.K, -100, CoordinationSystem.Global);
//l/oad2.Force = new Force(0, 100, 100, 0, 0, 0);
//load2.ForceIsoLocation = new IsoPoint(0.5, 0, 0);
elm.Loads.Add(load);
model.Elements.Add(elm);
model.Nodes.Add(n1, n2);
model.Solve_MPC();
var fnc = new Func <double, double>(x =>
{
try
{
var xi = elm.LocalCoordsToIsoCoords(x);
var frc = elm.GetExactInternalForceAt(xi[0]);
return(frc.Fz);
}
catch
{
return(0);
}
});
Controls.FunctionVisualizer.VisualizeInNewWindow(fnc, 1E-6, l - 1E-6, 500);
}
public static void TestFixedInternalForce2()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.UniformLoad(LoadCase.DefaultLoadCase, -Vector.J, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -0.5774 });
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = w * (length / 2 - x);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: 0, fy: vi, fz: 0, mx: 0, my: 0, mz: mi);
var d = testFrc.FirstOrDefault(i => i.Item1 == DoF.Rz).Item2 + exactFrc.Mz;
if (Math.Abs(d) > 1e-5)
{
}
}
}
public void LoadInternalForce_uniformload_truss()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var nodes = new Node[2];
var l = 4;
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.UniformLoad(LoadCase.DefaultLoadCase, Vector.I, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.TrussHelper(elm);
for (var x = 0.0 + 1e-6; x <= l - 1e-6; x += 0.1)
{
var local = x;
var iso = elm.LocalCoordsToIsoCoords(x);
var test = hlpr.GetLoadInternalForceAt(elm, u1, iso).FirstOrDefault(i => i.Item1 == DoF.Dx).Item2;
var exact = (w * l - x * l) / 2.0;
Assert.IsTrue(test.FEquals(exact, 1e-5), "invalid value");
}
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirY_My_End()
{
var l = 4.0;
var w = 2.0;
var a = l;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(l, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var f = new Force(0, 0, 0, 0, w, 0);
var loc = new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]);
var u1 = new Loads.ConcentratedLoad(f, loc, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var d0 = Force.Zero;
var d1 = loads[1] - f;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadInternalForce_uniformload_eulerbernoullybeam_dirZ()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.UniformLoad(LoadCase.DefaultLoadCase, -Vector.J, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = -w * (length / 2 - x);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: vi, fz: 0, mx: 0, my: 0, mz: mi);
var dm = Math.Abs(testFrc.Mz) - Math.Abs(exactFrc.Mz);
var df = Math.Abs(testFrc.Fy) - Math.Abs(exactFrc.Fy);
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] - f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value");
}
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirY_My()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 2.123; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, 0, w, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
//foreach (var x in CalcUtil.Divide(length, 10))
{
var x = 2.4;
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ma = w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = w / (L * L) * (3 * a * a - 2 * a * L);
var ra = -6 * w * a / (L * L * L) * (L - a); //R1
var rb = 6 * w * a / (L * L * L) * (L - a); //R1
mi = ma + ra * x - ((x > forceLocation) ? w : 0.0);
vi = ra;
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: -mi, mz: 0);
var dm = Math.Abs(testFrc.My) - Math.Abs(exactFrc.My); //regarding value
var df = Math.Abs(testFrc.Fz) - Math.Abs(exactFrc.Fz); //regarding value
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value"); //regarding sign
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value"); //regarding sign
}
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirY_Fz_Start()
{
//concentrated load applies on location xi=-1, then equivalent nodal loads at start node should be same as concentrated load
var w = 2.0;
var a = 0;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad(new Force(0, 0, -w, 0, 0, 0), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var d0 = loads[0] - u1.Force;
var d1 = Force.Zero;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirZ_fy()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, -w, 0, 0, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Z, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
//https://www.engineeringtoolbox.com/beams-fixed-both-ends-support-loads-deflection-d_809.html
var mi = 0.0;
var vi = 0.0;
{
var a = forceLocation;
var b = L - a;
var ma = -w * a * b * b / (L * L);
var mb = -w * a * a * b / (L * L);
var mf = 2 * w * a * a * b * b / (L * L * L);
double x0, x1, y0, y1;
if (x < forceLocation)
{
x0 = 0;
x1 = forceLocation;
y0 = ma;
y1 = mf;
}
else
{
x0 = forceLocation;
x1 = L;
y0 = mf;
y1 = mb;
}
var m = (y1 - y0) / (x1 - x0);
mi = m * (x - x0) + y0;
var ra = w * (3 * a + b) * b * b / (L * L * L); //1f
var rb = w * (a + 3 * b) * a * a / (L * L * L); //1g
if (x < forceLocation)
{
vi = ra;
}
else
{
vi = -rb;
}
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: vi, fz: 0, mx: 0, my: 0, mz: +mi);
var dm = Math.Abs(testFrc.Mz) - Math.Abs(exactFrc.Mz);
var df = Math.Abs(testFrc.Fy) - Math.Abs(exactFrc.Fy);
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value");
}
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirZ_Fy()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
// ^y w
// | ||
// | \/
// ====================================== --> x
// /
// /z
var w = 2.0;
var a = 2;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad(new Force(0, -w, 0, 0, 0, 0), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var ma = w * a * b * b / (L * L);
var mb = w * a * a * b / (L * L);
var ra = w * (3 * a + b) * b * b / (L * L * L); //1f
var rb = w * (a + 3 * b) * a * a / (L * L * L); //1g
var expectedF0 = new Force(0, -ra, 0, 0, 0, -ma);
var expectedF1 = new Force(0, -rb, 0, 0, 0, mb);
/*
* var m1 = -w * L * L / 12;
* var m2 = w * L * L / 12;
*
* var v1 = -w * L / 2;
* var v2 = -w * L / 2;
*/
var d0 = loads[0] - expectedF0;
var d1 = loads[1] - expectedF1;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirZ_Mz()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
// ^
// ^m m0 ^
// | /z |
// | / |
// ====================================== --> x
//
var w = 2.0;
var a = 1.234560;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad(new Force(0, 0, 0, 0, 0, w), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var ma = -w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = w / (L * L) * (3 * a * a - 2 * a * L);
var ra = 6 * w * a / (L * L * L) * (L - a); //R1
var rb = -6 * w * a / (L * L * L) * (L - a); //R1
var expectedR1 = new Force(0, ra, 0, 0, 0, ma); //expected reaction 1
var expectedR2 = new Force(0, rb, 0, 0, 0, -mb); //expected reaction 2
/*
* var m1 = -w * L * L / 12;
* var m2 = w * L * L / 12;
*
* var v1 = -w * L / 2;
* var v2 = -w * L / 2;
*/
var d0 = loads[0] + expectedR1;
var d1 = loads[1] + expectedR2;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadInternalForce_concentratedLLoad_Shaft_Mx()
{
//internal force of 2 node truss with concentrated load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, w, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new ShaftHelper(elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
var a = forceLocation;
var b = L - a;
var ra = (1 - (a / L)) * w;
var rb = (1 - (b / L)) * w;
mi = ra + ((x > forceLocation) ? -w : 0.0);
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: -mi, my: 0, mz: 0);
var df = Math.Abs(testFrc.Mx) - Math.Abs(exactFrc.Mx);
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value");
}
}
public void LoadInternalForce_concentratedLLoad_truss_Fx()
{
//internal force of 2 node truss with concentrated load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(w, 0, 0, 0, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new TrussHelper();
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ra = (1 - (a / L)) * w;
var rb = (1 - (b / L)) * w;
mi = ra + ((x > forceLocation) ? -w : 0.0);
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: -mi, fy: 0, fz: vi, mx: 0, my: 0, mz: 0);
var df = testFrc.FirstOrDefault(i => i.Item1 == DoF.Dx).Item2 + exactFrc.Fx;
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirY_My()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, 0, w, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ma = -w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = -w / (L * L) * (3 * a * a - 2 * a * L);
//var m = (y1 - y0) / (x1 - x0);
var ra = -6 * w * a / (L * L * L) * (L - a); //R1
var rb = -ra; //R2
mi = ma + ra * x + ((x > forceLocation) ? w : 0.0);
vi = ra;
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: -mi, mz: 0);
var dm = testFrc.FirstOrDefault(i => i.Item1 == DoF.Ry).Item2 - exactFrc.My;
var df = testFrc.FirstOrDefault(i => i.Item1 == DoF.Dz).Item2 + exactFrc.Fz;
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
}
public void eulerbernoullybeam_dirZ()
{
var w = 2.0;
var a = 4;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Z, elm);
for (var i = 0.0; i <= 1; i += 0.01)
{
var x = i * L;
var iso = elm.LocalCoordsToIsoCoords(x);
var n = hlpr.GetNMatrixAt(elm, iso);
var n1 = n[0, 0];
var m1 = n[0, 1];
var n2 = n[0, 2];
var m2 = n[0, 3];
var n1p = n[1, 0];
var m1p = n[1, 1];
var n2p = n[1, 2];
var m2p = n[1, 3];
var xi = iso[0];
var n1e = 0.25 * (2 - 3 * xi + xi * xi * xi);
var m1e = 0.125 * L * (1 - xi - xi * xi + xi * xi * xi);
var n2e = 0.25 * (2 + 3 * xi - xi * xi * xi);
var m2e = 0.125 * L * (-1 - xi + xi * xi + xi * xi * xi);
var epsilon = 1e-5;
Assert.IsTrue(Math.Abs(n1 - n1e) < epsilon, "invalid value");
Assert.IsTrue(Math.Abs(n2 - n2e) < epsilon, "invalid value");
Assert.IsTrue(Math.Abs(m1 - m1e) < epsilon, "invalid value");
Assert.IsTrue(Math.Abs(m2 - m2e) < epsilon, "invalid value");
}
}